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Comparing causal parameters with many treatments and positivity violations

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Summary Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, each targeting a different treatment. Treatment-specific means are commonly used, but their identification requires a positivity assumption: every subject has a nonzero probability of receiving each treatment. This assumption is often implausible, especially when treatment can take many values. Causal parameters based on dynamic stochastic interventions offer robustness to positivity violations. However, comparing these parameters may fail to reflect the effects of the underlying target treatments because the parameters can depend on outcomes under nontarget treatments. To clarify when two parameters targeting different treatments yield a useful comparison of treatment efficacy, we propose a comparability criterion: if the conditional treatment-specific mean for one treatment is greater than that for another, then the corresponding causal parameter should also be greater. Many standard parameters fail to satisfy this criterion, but we show that only a mild positivity assumption is needed to identify parameters that yield useful comparisons. We then provide two simple examples that satisfy this criterion and are identifiable under the milder positivity assumption: trimmed and smooth-trimmed treatment-specific means with multivalued treatments. For smooth-trimmed treatment-specific means, we develop doubly robust-style estimators that attain parametric convergence rates under nonparametric conditions. We illustrate our methods with an analysis of dialysis providers in New York State.

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  • Cite Count Icon 60
  • 10.1097/md.0000000000004529
Comparative efficacy of interventions on nonalcoholic fatty liver disease (NAFLD)
  • Aug 1, 2016
  • Medicine
  • Ratree Sawangjit + 6 more

The prevalence of nonalcoholic fatty liver disease (NAFLD) has significantly increased over the last decades. Despite existence of several interventions, there remains unclear which interventions work the best. A systematic review and network meta-analysis of randomized trials comparing efficacy of all treatment options in NAFLD were performed to determine comparative efficacy and safety of interventions in the management of NAFLD. Several electronic databases were searched up to Nov 15, 2015. Outcomes include liver histological outcomes (i.e., fibrosis), all-cause mortality, cirrhosis, and safety. A network meta-analysis was applied to estimate pooled risk ratios (RR). Quality of evidence was assessed using GRADE criteria. A total of 44 studies (n = 3802) were eligible. When compared with placebo, obeticholic acid (OCA) was the only intervention that significantly improved fibrosis with RR (95% CI) of 1.91 (1.15, 3.16), while pentoxyfylline (PTX) demonstrated improved fibrosis without statistical significance with RR (95% CI) of 2.27 (0.81, 6.36). Only thiazolidinedione (TZD) and vitamin E use resulted in significant increase in resolution of NASH, while OCA, TZD, and vitamin E significantly improved other outcomes including NAS, steatosis, ballooning, and inflammation outcomes. Quality of evidence varied from very low (i.e., metformin, PTX on mean change of ballooning grade) to high (OCA, TZD, vitamin E on improving histological outcomes). Limitations of this study were lack of relevant long-term outcomes (e.g., cirrhosis, death, safety), possible small study effect, and few head-to-head studies. Our study suggests potential efficacy of OCA, TZD, and vitamin E in improving histologic endpoints in NAFLD. These findings are however based on a small number of studies. Additional studies are awaited to strengthen this network meta-analysis.

  • Research Article
  • Cite Count Icon 1
  • 10.1080/24709360.2024.2347709
Identification and responses to positivity violations in longitudinal studies: an illustration based on invasively mechanically ventilated ICU patients
  • Jan 2, 2024
  • Biostatistics & Epidemiology
  • Aksel K.G Jensen + 3 more

Identification and estimation of causal effects relies on the positivity assumption, which states that there should be some positive probability of having each treatment level of interest, regardless of covariate levels. Violations of positivity can lead to both non-identified target causal parameters, estimator bias and inflated variance. We discuss reasons for and responses to positivity violations when the causal effect of interest involves treatments or exposures at multiple time points. For illustration, we use a data example involving the cumulative effect of controlling arterial oxygen tension over time on death among ICU patients receiving invasive mechanical ventilation. We distinguish between practical (by chance) violations that relate to sample size and structural violations in which certain treatment levels occur with zero probability for certain covariate levels. We focus on responses that either redefines the target population, e.g. via trimming or redefines the intervention making it more dynamic or more stochastic. Supported by a simulation study, we illustrate how these responses help restore needed positivity but also modify the target causal parameter. We further introduce an inability to intervene variable and show how such a variable will often be a time-dependent confounder and essential when addressing structural positivity violations in longitudinal settings.

  • Research Article
  • Cite Count Icon 6
  • 10.1093/jrsssa/qnae084
Synthesis estimators for transportability with positivity violations by a continuous covariate.
  • Sep 2, 2024
  • Journal of the Royal Statistical Society. Series A, (Statistics in Society)
  • Paul N Zivich + 5 more

Studies intended to estimate the effect of a treatment, like randomized trials, may not be sampled from the desired target population. To correct for this discrepancy, estimates can be transported to the target population. Methods for transporting between populations are often premised on a positivity assumption, such that all relevant covariate patterns in one population are also present in the other. However, eligibility criteria, particularly in the case of trials, can result in violations of positivity when transporting to external populations. To address nonpositivity, a synthesis of statistical and mathematical models can be considered. This approach integrates multiple data sources (e.g. trials, observational, pharmacokinetic studies) to estimate treatment effects, leveraging mathematical models to handle positivity violations. This approach was previously demonstrated for positivity violations by a single binary covariate. Here, we extend the synthesis approach for positivity violations with a continuous covariate. For estimation, two novel augmented inverse probability weighting estimators are proposed. Both estimators are contrasted with other common approaches for addressing nonpositivity. Empirical performance is compared via Monte Carlo simulation. Finally, the competing approaches are illustrated with an example in the context of two-drug vs. one-drug antiretroviral therapy on CD4 T cell counts among women with HIV.

  • Research Article
  • Cite Count Icon 1
  • 10.1007/s11062-016-9578-6
Comparative Efficacy of Pharmacological Treatment of Absence Epilepsy with Typical and Deviating (Complex) EEG Patterns
  • Apr 1, 2016
  • Neurophysiology
  • V I Maloletnev + 2 more

In a group of 96 children and teenagers suffering from absence epilepsy, we compared the efficacy of treatment with a valproic acid derivative, Depakin (D). In 72 patients of group 1, the EEGs contained typical bursts similar to absence seizure phenomena (generalized 3–4 Hz spike/wave complexes, SWCs). In 24 patients, these EEG phenomena were combined with other types of epileptiform elements (generalized and focal irregular peak/wave complexes, single and grouped sharp waves, spikes, polyspikes, etc.). It was found that pharmacotherapy with D effectively eliminated SWCs generated in the resting state of the patients; epileptiform phenomena provoked by hyperventilation and rhythmic photostimulation were noticeably more resistant from this aspect. The efficacy of treatment with D was considerably higher in group 1 (patients with the EEG patterns including only SWCs) than in group 2 (patients with deviating EEG patterns containing, together with SWCs, epileptiform elements of other types). Six months after the D therapy initiation, complete elimination of typical 3–4 Hz SWCs was observed in 63.9% of group-1 patients and in 41.7% of group-2 patients.

  • Research Article
  • 10.1097/ju.0000000000000715.02
Re: Comparative Efficacy and Safety of New Surgical Treatments for Benign Prostatic Hyperplasia: Systematic Review and Network Meta-Analysis.
  • Jan 7, 2020
  • The Journal of urology
  • Steven A Kaplan

Re: Comparative Efficacy and Safety of New Surgical Treatments for Benign Prostatic Hyperplasia: Systematic Review and Network Meta-Analysis.

  • Discussion
  • Cite Count Icon 4
  • 10.3168/jds.s0022-0302(05)72832-0
Letter to the Editor: Concerning an Article Comparing the Efficacy of Local and Systemic Treatment of Clinical Mastitis
  • May 1, 2005
  • Journal of Dairy Science
  • Satu Pyörälä

Letter to the Editor: Concerning an Article Comparing the Efficacy of Local and Systemic Treatment of Clinical Mastitis

  • Research Article
  • Cite Count Icon 559
  • 10.1177/0962280210386207
Diagnosing and responding to violations in the positivity assumption.
  • Oct 28, 2010
  • Statistical Methods in Medical Research
  • Maya L Petersen + 4 more

The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated and real data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative projection function to define the target parameter within a marginal structural working model, restriction of the sample, and modification of the target intervention. All of these approaches can be understood as trading off proximity to the initial target of inference for identifiability; we advocate approaching this tradeoff systematically.

  • Research Article
  • Cite Count Icon 3
  • 10.2147/clep.s427933
Effects of Adjusting for Instrumental Variables on the Bias and Precision of Propensity Score Weighted Estimators: Analysis Under Complete, Near, and No Positivity Violations.
  • Nov 1, 2023
  • Clinical Epidemiology
  • Byeong Yeob Choi + 1 more

To demonstrate that using an instrumental variable (IV) with monotonicity reduces the accuracy of propensity score (PS) weighted estimators for the average treatment effect (ATE). Monotonicity in the relationship between a binary IV and a binary treatment variable is an important assumption to identify the ATE for compliers who would only take treatment when encouraged by the IV. We perform theoretical and numerical investigations to study the impact of using the IV that satisfies monotonicity on the PS of treatment in terms of the positivity assumption, which requires that the PS be strictly between 0 and 1, and the accuracy of PS weighted estimators. Two versions of monotonicity that result in one-sided or two-sided noncompliance are considered. The PS adjusting for the IV always violates the positivity assumption when noncompliance occurs in one direction (one-sided noncompliance) and is more extreme than without the IV under two-sided noncompliance. These results are valid if the probability of being encouraged to get treatment and the compliance score, the probability of being a complier, are strictly between 0 and 1. Using a binary IV with monotonicity as a covariate for the PS model makes the estimated PSs unnecessarily extreme, reducing the accuracy of the PS weighted estimators.

  • Research Article
  • Cite Count Icon 23
  • 10.1007/s00330-023-09908-2
Ultrasound-guided microwave ablation versus surgery for solitary T1bN0M0 papillary thyroid carcinoma: a prospective multicenter study.
  • Aug 7, 2023
  • European radiology
  • Mo-Han Guo + 17 more

Microwave ablation (MWA) has emerged as a minimally invasive technology for papillary thyroid microcarcinoma (PTMC), but it has not been widely applied to treat T1bN0M0 PTC with high-level evidence. This study was designed to compare the real-world efficacy and safety of MWA or surgery for treating T1bN0M0 PTC. From December 2019 to April 2021, 123 continuous unifocal T1bN0M0 PTC patients without lymph node metastasis (LNM) or distant metastasis (DM) were included from 10 hospitals. Patients were allocated into the MWA or surgery group based on their willingness. The main outcomes were local tumour progression (LTP), new thyroid cancer, LNM, and DM. The secondary outcomes included changes in tumour size and volume, complications, and cosmetic results. Subgroup analyses were conducted to identify influencing factors. Fifty-two patients chose MWA, and 71 patients chose surgery. Patients had similar demographic information and tumour characteristics in the two groups. The follow-up durations after MWA and surgery were 10.6 ± 4.2 and 10.4 ± 3.4 months, respectively. The LNM rate was 5.8% in the MWA group and 1.4% in the surgery group (p= 0.177). No LTP, new thyroid cancer, or distant metastasis (DM) occurred in either group. Five (9.6%) of the 52 patients in the MWA group and 8 (11.3%) of the 71 patients in the surgery group had complications (p= 0.27). Better cosmetic results were found in the MWA group (p< 0.01). MWA achieved comparable short-term treatment efficacy with surgery. MWA might be an optional choice for surgery for low-risk T1bN0M0 PTC but concerns about LNM need to be studied further. MWA achieved comparable short-time treatment efficacy with surgery. MWA might be an optional choice for surgery for low-risk T1bN0M0 PTC. • MWA achieved comparable short-term treatment efficacy with surgery. MWA might be an optional choice for surgery for low-risk T1bN0M0 PTC but concerns about LNM need to be studied further. • The complication rate in the surgery group was higher than that in the MWA group without a significant difference. • There was no statistically significant difference in the LNM rate between the MWA and surgery groups.

  • Research Article
  • Cite Count Icon 4
  • 10.1159/000534747
Comparison of Efficacy and Safety between Carboplatin-Etoposide and Cisplatin-Etoposide Combination Therapy in Patients with Advanced Neuroendocrine Carcinoma: A Retrospective Study
  • Oct 30, 2023
  • Oncology
  • Hiroo Imai + 11 more

Introduction: Neuroendocrine carcinoma (NEC) is characterized by a poor prognosis and is generally treated with platinum and etoposide combination therapy as first-line chemotherapy. However, it remains uncertain whether carboplatin and etoposide combination therapy (CE) and cisplatin and etoposide combination therapy (PE) have comparable treatment efficacy. In this retrospective analysis, we compared the efficacy and safety of CE and PE in patients with NEC. Methods: We retrospectively reviewed the patient’s clinical record from 2005 to 2022 at the Department of Medical Oncology, Tohoku University Hospital. Patients who received either CE or PE were included in the study. Statistical analyses were performed using JMP Pro 16.0 (SAS Institute Inc., Cary, NC, USA). Results: A total of 104 patients were enrolled, with 73 patients assigned to the CE group and 31 patients assigned to the PE group. Statistically, the response rate, progression-free survival time and overall survival time were 42.6%, 5.1 months (95% CI: 3.5–6.3) and 13.6 months (95% CI: 8.9–17.4), respectively, in the CE groups and 44.4%, 5.6 months (95% CI: 3.1–7.0) and 12.5 months (95% CI: 11.2–14.6), respectively, in the PE groups. There was no significant difference in treatment efficacy between the CE and the PE groups. However, the number of patients with elevated creatinine (3.35 mg/dL and 3.88 mg/dL in 2 patients, respectively) was significantly higher in the PE group than in the CE group. Conclusion: The efficacy of CE and PE in patients with NEC is comparable. However, the incidence of renal dysfunction was found to be significantly higher in the PE group than in the CE group.

  • Research Article
  • Cite Count Icon 2
  • 10.1007/s40279-025-02179-5
Comparative Efficacy and Acceptability of Non-surgical Treatments with or without Exercise for Diastasis Recti Abdominis in Postpartum Women: A Network Meta-Analysis of Randomized Controlled Trials.
  • Jan 29, 2025
  • Sports medicine (Auckland, N.Z.)
  • Wen-Chieh Wu + 7 more

Diastasis recti abdominis (DRA), commonly occurring in postpartum women, is not only an aesthetic issue but is also highly associated with functional impairments. Various conservative treatment modalities have been employed in clinical practice to alleviate DRA. However, the comparative efficacy of these non-surgical treatments for improving the inter-recti distance (IRD) remains to be determined. This current network meta-analysis (NMA) aims to compare the efficacy and acceptability of different non-surgical treatments with or without exercise for improving DRA in postpartum women. This NMA adhered to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. ClinicalKey, Cochrane Library, CINAHL, Embase, PubMed, Web of Science, and ClinicalTrials.gov were systematically searched for randomized controlled trial (RCT) studies up to April 2024. The analysis included studies that met the following criteria: (1) postpartum women diagnosed with DRA defined as an IRD greater than 2cm; (2) intervention: any non-surgical treatments for at least 2weeks; (3) comparator: no-treatment control; and (4) outcome: changes in IRD and acceptability. The relative efficacy between the non-surgical treatments tested and the probability of treatments were evaluated. Twenty-one RCTs comprising 1195 participants aged from 18 to 45years old were included. The forest plot revealed that exercise coupling with neuromuscular electrical stimulation systems (NMES) [mean difference (MD) - 1.12cm, 95% confidence interval (CI) - 1.66 to - 0.58], acupuncture (MD - 0.81cm, 95% CI - 1.54 to - 0.08), corset (MD - 0.65cm, 95% CI - 1.24 to - 0.06), and exercise alone (MD - 0.48cm, 95% CI - 0.80 to - 0.16) led to significant reductions in IRD compared with control. Further, the treatment ranking indicated that the combination of NMES with exercise has the highest probability (91.0%) of being the best treatment for reducing IRD, followed by acupuncture with exercise (71.1%). Treatments combined with exercise demonstrated better rankings for reducing IRD than individual treatments without exercise. Acceptability did not significantly differ between the groups. This NMA encountered limitations due to participant variability, differing measurement methods, and sparse data, necessitating careful interpretation of findings regarding postpartum DRA interventions. This NMA suggests NMES combined with exercise as the best treatment tested for DRA in postpartum women. CRD42024541345.

  • Research Article
  • Cite Count Icon 38
  • 10.1136/bmjopen-2013-004285
Comparative efficacy and safety of treatments for localised prostate cancer: an application of network meta-analysis
  • May 1, 2014
  • BMJ open
  • Tengbin Xiong + 5 more

ContextThere is ongoing uncertainty about the optimal management of patients with localised prostate cancer.ObjectiveTo evaluate the comparative efficacy and safety of different treatments for patients with localised prostate cancer.DesignSystematic review...

  • Research Article
  • Cite Count Icon 4
  • 10.12671/jksf.2001.14.2.189
Treatment of subtrochanteric fracture - Comparison of treatment efficacy according to internal fixation device -
  • Jan 1, 2001
  • Journal of the Korean Society of Fractures
  • Taek Rim Yoon + 4 more

Treatment of subtrochanteric fracture - Comparison of treatment efficacy according to internal fixation device -

  • Research Article
  • Cite Count Icon 11
  • 10.1136/bmjopen-2022-068313
Comparative efficacy, cognitive effects and acceptability of electroconvulsive therapies for the treatment of depression: protocol for a systematic review and network meta-analysis
  • Dec 1, 2022
  • BMJ Open
  • Stevan Nikolin + 10 more

IntroductionThere have been important advances in the use of electroconvulsive therapy (ECT) to treat major depressive episodes. These include variations to the type of stimulus the brain regions stimulated, and...

  • Research Article
  • Cite Count Icon 64
  • 10.1097/00004850-200609000-00008
Escitalopram versus venlafaxine XR in the treatment of depression
  • Sep 1, 2006
  • International Clinical Psychopharmacology
  • Stuart A Montgomery + 1 more

This article reanalyses and reviews data from the two published randomized clinical trials comparing escitalopram and venlafaxine XR in the treatment of patients with major depressive disorder. The aim was to further compare the efficacy and tolerability of escitalopram and venlafaxine XR and to assess the impact of the two treatments on the patient's quality of life, as well as the benefit/risk of treatment. A total of 243 escitalopram-treated patients and 240 venlafaxine XR-treated patients were included in this analysis. Comparable treatment efficacy was achieved with respect to the prospectively defined primary efficacy endpoint (mean change from baseline in Montgomery Asberg Depression Rating Scale (MADRS) total score at week 8). An analysis of the outcome at the end of study by baseline severity showed that the treatment difference became greater the more severely depressed the patients were at baseline. At the highest permitted doses, in the subgroup of patients who were severely depressed (baseline MADRS > or =30), patients treated with escitalopram had a statistically significantly greater improvement (P<0.05) in mean MADRS total scores than patients treated with venlafaxine XR at endpoint. For these patients, treatment with 20 mg/day escitalopram resulted in a statistically significantly (P<0.05) higher remission rate at week 8 (47%) than treatment with venlafaxine XR (29%). This difference was confirmed by the analysis of the pooled data, which showed that patients in the escitalopram group had a significantly (P<0.05) higher mean number of depression-free days (30.4 days) than those in the venlafaxine XR group (26.2 days) over the 8-week period. The relative benefit of escitalopram versus venlafaxine XR was 1.46, indicating that a patient was more likely to benefit from treatment with escitalopram. The proportions of patients who withdrew owing to adverse events were 7.5% in the escitalopram group and 11.2% in the venlafaxine XR group. The mean number of discontinuation emergent signs and symptoms in the venlafaxine XR group (mean: 5.0) was significantly (P<0.001) higher than for the escitalopram group (mean: 2.4).

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